Answer
(a.) Underestimate by $1\%$.
(b.) Year $=2020$.
Work Step by Step
The given formula is
$M=-0.4x+48$
Where $M$ is the percentage of married filers.
$x$ is years after $1985$.
(a.) For $2005$.
$x=2005-1985$
$x=20$
Substitute the value of $x$ into formula.
$M=-0.4(20)+48$
$M=-8+48$
$M=40$
The model underestimated by $=41-40=1\%$.
(b.) Plug the value of $M=34$.
$34=-0.4x+48$
Add $0.4x-34$ to both sides.
$34+0.4x-34=-0.4x+48+0.4x-34$
Simplify.
$0.4x=14$
Divide both sides by $0.4$.
$\frac{0.4x}{0.4}=\frac{14}{0.4}$
Simplify.
$x=35$
The year is $1985+35 = 2020$.
